My 2 cents,
1. Although rated at 300cpi, I wonder if it would be realistic. I had to move significant distance (about 0.5mm) before the mouse actually register the move (not sure whether it's hardware or driver limitation).
2. Mouse actually send 'relative move', i.e., how many pulse in x or y since last update. No direct link to screen size.
3. Not necessarily. Mouse communication protocol is almost standard. Simple microcontroller can read the protocol and drive an LCD or LED display.
Like I said, my 2 cents